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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 376768db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
376768.db2 | 376768db1 | \([0, -1, 0, -7159713, 8735325089]\) | \(-1041220466500/242597383\) | \(-9457013949855756648448\) | \([2]\) | \(20643840\) | \(2.9361\) | \(\Gamma_0(N)\)-optimal |
376768.db1 | 376768db2 | \([0, -1, 0, -120324673, 508041761601]\) | \(2471097448795250/98942809\) | \(7714044672533946564608\) | \([2]\) | \(41287680\) | \(3.2827\) |
Rank
sage: E.rank()
The elliptic curves in class 376768db have rank \(0\).
Complex multiplication
The elliptic curves in class 376768db do not have complex multiplication.Modular form 376768.2.a.db
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.